find the equation for the ellipse

Question

A railroad tunnel is shaped like a semiellipse as shown below. 

 

The height of the tunnel at the center is 27 ft and the vertical clearance must be 9 ft at a point 24 ft from the center. Find an equation for the ellipse.

Answer 1

A rail road tunnel is shaped like a semiellipse.

The vertices of the semi ellipse on the x axis.

The horizontal ellipse vertices are on the x axis.

So the ellipse is horizontal.

Standardform of horizontal ellipse is

In this case

Maximum y value is 9.

Substitute the x,y and b in above standard form .

Substitute the a,b values in standard form.

Threfore ,the ellipse equation is